Abstract We develop a deformation quantization approach to quantum mechanics that exhibits a nonzero minimal uncertainty in position through the modification of commutation relations for the operators of position and momentum. Deformation quantization is a method of quantizing a classical Hamiltonian system by suitably deforming the Poisson algebra of the system. The developed theory of deformation quantization is non-formal. An appropriate integral formula for the star-product is introduced, along with a suitable space of functions on which the star-product is well defined. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in momentum space is presented. Finally, an example of states of maximal localization is given in terms of generalized Wigner functions.Abstract We develop a deformation quantization approach to quantum mechanics that exhibits a nonzero minimal uncertainty in position through the modification of commutation relations for the operators of position and momentum. Deformation quantization is a method of quantizing a classical Hamiltonian system by suitably deforming the Poisson algebra of the system. The developed theory of deformation quantization is non-formal. An appropriate integral formula for the star-product is introduced, along with a suitable space of functions on which the star-product is well defined. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in momentum space is presented. Finally, an example of states of maximal localization is given in terms of generalized Wigner functions.

Journal of Physics Conference SeriesDec 1, 20240 citations

Basic-deformed quantum mechanics

A. Lavagno

arXiv:0911.1627Reports on Mathematical PhysicsAug 1, 200941 citations

Quantum mechanics with spontaneous localization revisited

T. Weber

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BOct 1, 19916 citations

TT¯ deformation on multiquantum mechanics and regenesis

Song He, Zhuo-Yu Xian

We study the $T\overline{T}$ deformation on multiquantum mechanical systems. By introducing dynamical coordinate transformation, we reformulate the one-dimensional $T\overline{T}$ deformation of generic quantum mechanical systems, which is consistent with the previous proposal in the literature. We further study the thermo-field-double state under the $T\overline{T}$ deformation on these systems, which include the conformal quantum mechanical system, the Sachdev-Ye-Kitaev model, and the model satisfying the eigenstate thermalization hypothesis. We find common regenesis phenomena in which the signal injected into one local system can regenerate from the other local system. From the ${\mathrm{AdS}}_{2}/{\mathrm{CFT}}_{1}$ perspective, we study the deformation of Jackiw-Teitelboim gravity governed by Schwarzian action and find that these regenesis phenomena are realized by exchanging boundaries graviton via the nonlocal $T\overline{T}$ coupling.We study the $T\overline{T}$ deformation on multiquantum mechanical systems. By introducing dynamical coordinate transformation, we reformulate the one-dimensional $T\overline{T}$ deformation of generic quantum mechanical systems, which is consistent with the previous proposal in the literature. We further study the thermo-field-double state under the $T\overline{T}$ deformation on these systems, which include the conformal quantum mechanical system, the Sachdev-Ye-Kitaev model, and the model satisfying the eigenstate thermalization hypothesis. We find common regenesis phenomena in which the signal injected into one local system can regenerate from the other local system. From the ${\mathrm{AdS}}_{2}/{\mathrm{CFT}}_{1}$ perspective, we study the deformation of Jackiw-Teitelboim gravity governed by Schwarzian action and find that these regenesis phenomena are realized by exchanging boundaries graviton via the nonlocal $T\overline{T}$ coupling.

arXiv:2104.03852Physical review. D/Physical review. D.Aug 10, 202214 citations

DEFORMED OPEN QUANTUM SYSTEMS

Аурелиан Исар

International Workshop on New Applications of Nuclear FissionSep 1, 20041 citation

We study the

T\overline{T}

deformation on multiquantum mechanical systems. By introducing dynamical coordinate transformation, we reformulate the one-dimensional

T\overline{T}

deformation of generic quantum mechanical systems, which is consistent with the previous proposal in the literature. We further study the thermo-field-double state under the

T\overline{T}

deformation on these systems, which include the conformal quantum mechanical system, the Sachdev-Ye-Kitaev model, and the model satisfying the eigenstate thermalization hypothesis. We find common regenesis phenomena in which the signal injected into one local system can regenerate from the other local system. From the

{\mathrm{AdS}}_{2}/{\mathrm{CFT}}_{1}

perspective, we study the deformation of Jackiw-Teitelboim gravity governed by Schwarzian action and find that these regenesis phenomena are realized by exchanging boundaries graviton via the nonlocal

T\overline{T}

coupling.